There are three reasons commonly given for practicing these in my school:

Tradition (it's part of the art)

In case someone ever uses one on you, you'll know what it looks like and be prepared to counter it.

Improves your balance and muscle coordination.

It is explicitly stated by my instructor that you are unlikely to ever actually use the advanced spinning kicks in reality (reality here being defined as "in self defense situations," not in a ring or a duel).

I see the first one: There's more to a martial art than what is currently considered practical. The second one I consider a low-margin game considering how few people seem to use them, though I understand it (e.g., if you've never seen a passata soto, you can end up quite dead to it before realizing how to counter it).

I am wondering, however, if there is any validity to the last one or if there might be other reasons that we haven't discussed for training in these techniques?

4 Answers
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I think this nicely illustrates the mental conflict between drills and practical application.

Consider one of the key points of a high spinning kick (taekwondo in my case but the commonality with hapkido is obvious): a high spin draws your upper body down and away from your target. Obviously, the movement of your upper body will differ based on flexibility and the situation.

Now consider a threat: a baseball bat swung at your face. In that case, you are naturally inclined to withdraw the upper body and counter-attack with the big muscles in your legs. I find that a variant of the sparring back spinning kick serves as an acceptable compromise between speed and power: the back kick provides the power and the spin allows me to position the strike at an off angle.

Is this a risky maneuver? Of course. It requires finicky timing. However, it accomplishes one of my major goals (i.e., keeping the bat away from my face) and there's an excellent chance that I'm going to hit the bad guy somewhere and quite hard.

Nothing in the real world will ever match your training. By learning a variety of techniques, you have the fundamentals required to adjust and adapt to the situation at hand.

Or, in this case, at foot.

EDIT: I found the link for the 2004 Olympic heavyweight match. In this case (at about 4:40), the Korean victor saw his opponent commit to an attack and was able to counter with a knockout. As always, you have to remember that sparring is not real life. That said, this video serves as a clear lesson that an aggressor is often more vulnerable than he realizes.

It is explicitly stated by my instructor that you are unlikely to ever actually use the advanced spinning kicks in reality (reality here being defined as "in self defense situations," not in a ring or a duel).

I have been thinking about your instructor's comment quite a lot lately. I have to agree that these are not techniques that you are likely to have to use in real life but not because they aren't practical. These are killing techniques. Look at the knockout in that video: a highly trained expert wearing full head protection was knocked unconscious with one blow. It is likely that a normal person would be dead or permanently disabled.

Hopefully, you'll never be in a position where that seems like a desirable outcome.

"In that case, you are naturally inclined to withdraw the upper body and counter-attack with the big muscles in your legs" -- That's not a _natural_response. It's a trained one. It's certainly not what I would have done when I had no training, and it's not what I do now, because it's not the training I received.
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TrevokeFeb 19 '12 at 2:56

@Trevoke, if you're speaking about the overall population, sure, they are not inclined to back kick. They are, however, inclined to get their head out of the way. The OP was asking from the point of view of someone who is being trained in spinning kicks and does not understand the motivation. That is not the average person. So, when I say "you" in that sentence, you can substitute "David H. Clements."
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Bob CrossFeb 19 '12 at 16:27

@Rophuine Sensible, no doubt about it! As I said, not what I would do, but that's because my body has been trained to do different things :)
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TrevokeFeb 20 '12 at 15:46

Awesome bout @BobCross - thanks for the link. Will have to show it to my kids. As an aside - did you see the pattern videos I popped up on our local TKD website? tkdbroxburn.co.uk/patterns.html (that isn't me in the videos, by the way :-)
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Rory AlsopFeb 22 '12 at 12:47

Everything you say is fairly accurate. There is one very interesting further use case, which expands on your idea of balance and muscle coordination - If you think of that sequence of movements as two-player drill, you can begin to examine it in a different light.

Theoretically: this particular low-spinning heel strike might be a follow-up to a high parry and a leg takedown. Practicing this particular sequence would teach you the exact sequence of movements needed to take down someone else.

There is an addition - these kicks are just small parts of a much more complete training curriculum. In martial arts, the whole is greater than the sum of the parts. Training all these kicks teaches you much more than just a bunch of kicks. But I can't answer that for you -- because that is the path you're on, and you have to find that answer within yourself.

Hook kick is very beneficial as both a "stealth technique" and if you have bad aim with a side kick.

Start by throwing a side kick that misses the opponent such that your foot is in front of his head (heel points to his head, toes point to the audience). If the side kick was high enough, and far enough from his head, he probably blocked the kick with a low block and his head is open, throw the hook part of the kick and you just hooked his head. 2 points for head contact.

Another trick is to use skips and scissors to break the distance quickly.

In many ways, what comes natural to us may not be natural to others. And vice-versa. As such there will be techniques you have to learn and teach that might not be great for you, but will be for your student. When it comes to the spinning techniques, my "grand-sensei", if you will, was a natural at them. My direct sensei much less so. And I am even less comfortable with them--but that may change with practice.

Even so, the spin techniques are very good stealth techniques. For example, a back-turn side kick or hook kick looks like someone is just trying to get away from you. When you have a foot in your side, you realize that wasn't the case after all.

As to whether something like that is practical now, you have to consider the environment where you expect to be fighting. Almost anything is practical when you have a ring with a flat surface. The choice of techniques that remain practical can be different if you are fighting in a train (moving platform, confined space, several obstructions). The same could be said about mountainous terrain or grassy fields (more traditional settings). I'd be inclined to argue that a spin kick of any sort would be problematic if you are on a moving platform.